Surface stress effect plays an important role in determining the properties of nanostructures. In lattice-mismatched 3D epitaxial systems, elastic relaxation could effectively reduce the natural misfit between the nanoisland and substrate. This work proposes a systematic study on the elastic relaxation in 3D epitaxial nanoisland with strain-dependent surface stress effect. The analytical methodology is formulated for general anisotropic nanostructures with general geometries (size and shape). An example of a copper cuboid is provided to demonstrate how the finite size and surface property of the nanoisland would influence the elastic relaxation between the nanoisland and substrate. The influence of surface stiffness is shown to be more significant in the lateral dimension than the height dimension. More importantly, this work indicates that surface stiffness becomes important to determine the overall property of the nanoisland when its size is lower than 10 nm, so surface stress should be considered to be strain-dependent in such situations. This would be important for the fabrication of high quality nanostructures. (C) 2014 Elsevier B.V. All rights reserved.